Sampling normalizing constants in high dimensions using inhomogeneous diffusions

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Abstract

Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on Rd. The main results are nonasymptotic variance and bias bounds, and a central limit theorem in the d→∞ regime. We demonstrate that a temporal discretization inherits the fluctuation properties of the underlying diffusion, which are controlled at a computational cost growing at most polynomially with d. The key technical steps include establishing Poincar\'e inequalities for time-marginal distributions of the diffusion and nonasymptotic bounds on deviation from Gaussianity in a martingale central limit theorem.
Original languageEnglish
Article number1612.07583
Number of pages77
JournalarXiv
Publication statusPublished - 22 Dec 2016

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